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arXiv · 2512.24522

Proper colorings of a graph in linear time using a number of colors linear in the maximum degree of the graph

Kritika Bhandari·Mark Huber
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Abstract

A new algorithm for exactly sampling from the set of proper colorings of a graph is presented. This is the first such algorithm that has an expected running time that is guaranteed to be linear in the size of a graph with maximum degree \( \Delta \) when the number of colors is greater than \( 3.637 \Delta + 1\).

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Kritika Bhandari, Mark Huber. 2025-12-30. Proper colorings of a graph in linear time using a number of colors linear in the maximum degree of the graph. https://arxiv.org/abs/2512.24522

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